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thechocoluver445
 2 years ago
If the direction angle of vector a is 100 degrees, with a magnitude of 8, and the direction angle of vector c is 60 degrees, with a mangitude of 13, find the magnitude of resultant a + c.
I know how to set this up and solve it, but for some reason I can't get the right answer.
thechocoluver445
 2 years ago
If the direction angle of vector a is 100 degrees, with a magnitude of 8, and the direction angle of vector c is 60 degrees, with a mangitude of 13, find the magnitude of resultant a + c. I know how to set this up and solve it, but for some reason I can't get the right answer.

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thechocoluver445
 2 years ago
Best ResponseYou've already chosen the best response.1Here's what I did: dw:1358034696496:dw \[x = \sqrt{8^2 + 13^2  2(8)(13)(\cos 140°)}\]

zepdrix
 2 years ago
Best ResponseYou've already chosen the best response.0Hmmm this is how I would do it :O So if we write our vectors in component form, we have,\[\large \vec{a}=8\cos100 \hat i+8\sin100 \hat j\]\[\large \vec c=13\cos60 \hat i+13\sin60 \hat j\]\[\large \vec a +\vec c=\color{#3366CF}{(8\cos100+13\cos60)\color{black}{\hat i}+(8\sin100+13\sin60)\color{black}{\hat j}}\] Hmm since 100 degrees isn't a nice special angle, we're going to get ugly decimal values it seems... So punch that into the calculator, then to get the MAGNITUDE of that vector we'll do uhhhh the thing, yah... I'm a little confused where your formula for x is coming from. It looks similar to the law of cosines. Maybe I just haven't done these types of problems in too long c: heh

thechocoluver445
 2 years ago
Best ResponseYou've already chosen the best response.1Yeah I used law of cosines. If I add up all of the things in your method, I don't get the correct answer.

zepdrix
 2 years ago
Best ResponseYou've already chosen the best response.0ah ok c: lemme take another shot at it. sec.

zepdrix
 2 years ago
Best ResponseYou've already chosen the best response.0Hmm I'm not quite sure :c In your attempt at the problem, where is the 140 degree angle coming from?

thechocoluver445
 2 years ago
Best ResponseYou've already chosen the best response.1180  40 = 140.

thechocoluver445
 2 years ago
Best ResponseYou've already chosen the best response.1(In the parallelogram)

mathmate
 2 years ago
Best ResponseYou've already chosen the best response.1Did you have a positive or negative value for cosine?

mathmate
 2 years ago
Best ResponseYou've already chosen the best response.1What did you get for the magnitude?

thechocoluver445
 2 years ago
Best ResponseYou've already chosen the best response.1It would be negative since the 140 is to the left of the y axis

mathmate
 2 years ago
Best ResponseYou've already chosen the best response.1Sounds good. So your magnitude is greater than 13? What did you get? Is it a matter of number of decimals?

mathmate
 2 years ago
Best ResponseYou've already chosen the best response.1@thechocoluver445 are you still there?

thechocoluver445
 2 years ago
Best ResponseYou've already chosen the best response.1It's supposed to be 9.8 but I keep getting 19. something!

thechocoluver445
 2 years ago
Best ResponseYou've already chosen the best response.1I'm pretty sure my way makes sense, but I don't know.

thechocoluver445
 2 years ago
Best ResponseYou've already chosen the best response.1I just realized that my way was correct. Since the resultant is opposite an obtuse angle, it must be the longest side of the triangle. Thus, 9.8 cannot be the right answer! So I was correct. Thanks to everyone for helping. :)

mathmate
 2 years ago
Best ResponseYou've already chosen the best response.119.8 is correct for the problem you have posted..

thechocoluver445
 2 years ago
Best ResponseYou've already chosen the best response.1The answer key was just wrong, lmao!

thechocoluver445
 2 years ago
Best ResponseYou've already chosen the best response.1Yeah, that's what I got lol!

thechocoluver445
 2 years ago
Best ResponseYou've already chosen the best response.1She probably just forgot the 1 before the 9.8 haha

mathmate
 2 years ago
Best ResponseYou've already chosen the best response.1The only thing you may want to check to see if there are typos. It is possible that they modified the question but forgot to modify the key (which is half of the current answer).

mathmate
 2 years ago
Best ResponseYou've already chosen the best response.1Oh, so it's not a printed key! That make it even more probably that the answer is wrong.
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